The function f(x) is defined by f(x)=⎧⎪⎨⎪⎩(x2+e12−x)−1,x≠2k,x=2.
If it is continuous from right at the point x=2, then k is equal to
A
0
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B
14
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C
−12
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D
None of these
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Solution
The correct option is B14 f(2)=k=limx→2+f(x) as f(x) is right continuous at x=2 ⇒k=limx→2+(x2+e12−(x))−1 =limh→0((2+h)2+e−1h)−1 =(4+e−∞)−1[∵e−∞→0] ⇒k=4−1=14